Swets et al (1961)

Key ideas

• continuity in stimulus-induced mental states• variability in these states• sensitivity (d’)• role of prior probability and payoffs• bias, criterion…• Bayesian inference• normative/optimal model, ideal observer

Your questions• How to get expected ROC given hypothetical underlying

distributions?• What is the meaning of the ‘spread’ or ‘variance’, and how

does this relate to performance?• What is ‘beta’ exactly and how does it relate to area under

curve?• How are ROC curves generated from a rating experiment?• How is the prior and/or placement of the criterion

determined by the subject? Is learning involved? If so in what way?

More questions

• When do we stay with a theory even if it isn’t a perfect fit and when do we reject it and seek another theory?

• How was it that the authors were able to reject the threshold theory even when their own data were and only so-so fit to their own theory?

• How do we generalize given the large individual differences in studies such as these?

• How do we distinguish between signals lost in noise and signals that decay before they can be reported?

Plan

• Go over the basic elements of the theory• Generate a hypothetical ROC curve• Consider effect of prior and payoff• Consider effect of unequal variance• Consider the data reported in the experiments

Key Concepts• Prior p(SN), p(N)• Likelihood fSN(x) = p(x|SN),

fN(x) = p(x|N)• likelihood ratio =

fSN(x)/fN(x)• Posterior p(SN|x), p(N|x)• Criterion, Beta• [Maximizing strategy

inherent in model vs. probability matching]

Subliminal Perception?

• “It may be, therefore, that subliminal perception exists only when a high criterion is incorrectly identified as a limen.”

More questions

• When do we stay with a theory even if it isn’t a perfect fit and when do we reject it and seek another theory?

• How was it that the authors were able to reject the threshold theory even when their own data were and only so-so fit to their own theory?

• How do we generalize given the large individual differences in studies such as these?

• How do we distinguish between signals lost in noise and signals that decay before they can be reported?